Statics and Dynamics of V-shaped Micro-beams Under Axial Forces

Abstract

Abstract We present an investigation into the static and dynamic behaviors of electrostatically actuated in-plane micro-electro-mechanical V-shaped micro-beam under axial loads. The micro-beams are actuated with two separate electrodes of uniform air-gap across their length. The effects of the initial rise and DC bias voltage are examined while varying the axial loads ranging from compressive to tensile. The numerical analysis is based on a nonlinear equation of motion of a shallow V-shaped micro-beam. The static equation is solved using a reduced-order model based on the Galerkin procedure. Then, the eigenvalue problem of the structure is solved for various equilibrium positions. The analytical model is validated by comparing to an experimental case study. The results show rich and diverse static and dynamic behavior. It is shown that the micro-beam may exhibit only pull-in or snap-through and pull-in instabilities. Various multi-state and hysterics behaviors are demonstrated when varying the actuation forces and the initial rise. High tunability is demonstrated when varying the axial and DC loads for the first two symmetric vibration modes. Such rich behavior can be very useful for high performance micro-scale applications designs.